Q.
For 0<θ<2π, four tangents are drawn at the four points (±3cosθ,±2sinθ) to the ellipse 9x2+4y2=1. If A(θ) denotes the area of the quadrilateral formed by these four tangents, th e minimum value of A(θ) is
We have,
Equation of ellipse 9x2+4y3=1
Equation of tangent at (3cosθ,2sinθ) is 3xcosθ+2ysinθ=1
Intercept of tangent is (3secθ,0) and (0,2cosecθ)
Area of quadrilateral =4×213secθ×2cosecθ =12secθcosecθ=sin2θ24
Minimum area =24